Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
488 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #34036674 | C2 | semidirect |
| 2. C2×#22627586 | C2 | semidirect |
| 3. #34036447 | C2 | semidirect |
| 4. #34036418 | C2 | semidirect |
| 5. #34036323 | C2 | semidirect |
| 6. #34036265 | C2 | semidirect |
| 7. #34036262 | C2 | semidirect |
| 8. #34036240 | C2 | semidirect |
| 9. #34036238 | C2 | semidirect |
| 10. #34036183 | C2 | semidirect |
| 11. #481×C293 | C2 | semidirect |
| 17. #22627623 | C22 | semidirect |
| 18. #22627620 | C22 | semidirect |
| 22. D4×Dic293 | C22 | semidirect |
| 27. #22627586 | C22 | semidirect |
| 31. #22627555 | C22 | semidirect |
| 32. #22627553 | C22 | semidirect |
| 35. #22627544 | C22 | semidirect |
| 37. #22627534 | C22 | semidirect |
| 40. #106×C293 | C22 | semidirect |
| 41. #102×C293 | C22 | semidirect |
| 92. D1172 | #41 | semidirect |
| 149. C293 | #3109 | semidirect |
| 154. #481 | D293 | semidirect |
| 184. #106 | C2×D293 | semidirect |
| 189. #102 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036674 | 2 |
| C2×#22627586 | 2 |
| #34036447 | 2 |
| #34036418 | 2 |
| #34036323 | 2 |
| #34036265 | 2 |
| #34036262 | 2 |
| #34036240 | 2 |
| #34036238 | 2 |
| #34036183 | 2 |
| #481×C293 | 2 |
| #3109 | 293 |